This is long, but I'd just like to give my experience, having watched almost all of TNG-era Star Trek and the Stargate franchise first-run. I will say off to bat that I like Star Trek more than Stargate, but recognize both as good sci-fi franchises (that did decline in their last few seasons).
I started watching Star Trek in the early '90s as a kid. I loved TNG and saw all the seasons I was too young to see/notice in syndication while the series was still airing new episodes. I watched TNG first-run, then Voyager first-run, then ENT first-run all through their run. DS9... I saw part of the first season but it bored me. I tuned in intermittantly in Season 3, more regularly I think with the spring eps/summer reruns, and watched it all through in Seasons 4-7 (I do regret not tuning in to Season 2, one of the most underrated Star Trek seasons). That's my Star Trek background.
I started watching Stargate SG-1 from the very beginning, on Showtime in 1997. Season 1 was pretty good for a sci-fi show, but the episodes were rather weak. Decent, but definately needed to grow. The cast was very likeable. Richard Dean Anderson, well known from MacGyver then, was likeable, presenting a competent military figure/team leader but also having sarcasm, and a flippant attitude. Both Carter & Jackson were likeable characters and the team had a great configuration of different positions/attitudes/skills. Teal'c was clearly the stock proud warrior.
I thought the Jaffa were going to end up like Klingons, but while Stargate's writers got more unoriginal and dull late in the franchise compared to even ENT's writers, the development of the Jaffa over the series was one of the things Stargate did best. The premise was very interesting, foot travel across space, villains that are parasites using humans as hosts and Egyptian mythology as their motif.
SG1 started to really grow with the final arc in Season 1. 4 linked episodes weaving together a mirror universe, the crooked politician's agenda against the SGC, and the Goa'uld invasion of Earth. Those kinds of arcs were not that widespread then (but were growing. Beyond B5, DS9 just did it with the 6 episode exile/retaking DS9 arc).
And overall by each season...
- It got noticeably better over Season 2, introducing the Tok'ra, the rogue Stargate operation, and the story quality was getting better.
- Season 3 got better; episodes finally felt fully polished. Apophis 2.0, though he looked stupid with the Seven of Nine ripoff on his face, was a far more interesting villain than Sokar (a proto-Anubis), who had a cool menace early on, his troops looked cool, but he was too one-note. The Goa'uld need face/personality to sell their side of the show.
- I personally liked Seasons 4-5 the most. There were many very good episodes. Apophis was replaced with Anubis at about the right time, and Anubis in the shadows, using agents was good, but the suspense about his face was contrived and the revelation was so lame. The explanation of Anubis' origin (he cheated on a test!) was dumb. "Watergate", "The Warrior", "The Sentinel", "2010"/"2001", "Window of Opportunity"... so many good episodes.
- I felt Season 6 was too bland (too many episodes set on Earth, a very disjointed 2 parter) and the leap to Earth having spaceships (Prometheus et al), while it seemed like a necessary step in storytelling, the development seemed paper-thin flimsy and came out of nowhere. It's all of a sudden "we have starships!". Oh, and Jonas Quinn as the wallpaper to read Daniel Jackson lines. Anubis was handled cool in Season 5, but once he became the top Goa'uld, he devolved into Sokar, just a faceless evil Emperor with melodramatic lines. Daniel Jackson ascended seemed a lame explanation, but it seemed like "whatever, so long as they bring him back". Tetronin and the Jaffa rebellion were good developments that really propelled part of the show that felt like it was stagnating.
- Season 7 had better quality stories than S6, but Anubis's menace seemed very contrived. Supersoldiers made it even more so. They looked for the Lost City (the billed mission that season) as much that season as OJ looked for "the real killer" in the decade he was free after his murder trial.
- I know many people end at Season 8 and hate the new order, but I actually felt the Farscape guy & Beau Bridges were good and the new menace, Ori, new mythology (Arthurian) blended together well. RDA > Farscape dude, but he was capable of carrying a show. BB almost = DD. Season 9 felt like a fresh wind. Season 8 felt very stale. The Goa'uld were no longer a menace, it was Replicators out the wazoo, and Anubis as a oooo scary ghost. For the first time, I lost interest in SG-1. "Moebius" was very good though. It felt like a show cruising sleepily towards its series finale.
Season 9 was the best season since S5. Most of the episodes were interesting (not "Prototype", AKA Anubis redux, though). The Ori felt like a very good menace (as strong as the Borg felt early on). Would've been nice to have Vala all season, but I understood her RL pregnancy forced her to be written out til S10.
- Season 10 wasn't as good. Some good episodes, lots of decent to mediocre episodes. The V lady as an Ori avatar, while she was easy on the eyes, felt like another contrived rapidly aging baby and an effort to create a Goa'uld System Lord like figure for the Ori (an Ori pope of sorts).
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Stargate Atlantis... saw the pilot, didn't care for it. The Marilyn Manson video extra as the Wraith queen seemed like such a lame ripoff (though TNG "Phantasms" ripped off a Tom Petty video) and it seemed too much like the EFC Season 5 Atavus. When the next episode was an utterly worn out sci-fi cliche, I tuned out. Only by seeing the 2-parter with the Genii & the hurricane, a real pale Wraith in "The Defiant One", and "The Brotherhood" was I hooked. I saw SGA Seasons 2-5.
- Yeah, I generally agree with people that Season 1, then 2 are the best. Late Season 1 is far better than the first half though.
(SPOILERS)
- Season 3... The Asuran Replicators were good initially, but they came to be so overused in their 1 short year, I was glad they got rid of them in Season 4. They pulled a Trip at the end of Season 3, but at least they were forced to undo it. Carson Beckett >>>>>>>>>> Keller. She sucked in Season 4, became tolerable in Season 5. Outside of Replicator overload and that Irr- jackass, most episodes in S3 were fairly good.
- Season 4... Carter didn't feel like a good fit. She was like Worf in DS9- didn't add anything. Many episodes tended to be blander too. I think this was the weakest season.
- Season 5, I know people hated the show getting its 3rd new leader in as many seasons (shades of EFC) but Robert Picardo (the Doctor) was the best person for it. A skilled actor, he can make likeable characters and made what could have been a woeful season enjoyable. Episodes were overall mediocre, but there were a lot of interesting concepts- the rogue Asgard, the secret Pegasus council, "Whispers" was a great atmospheric episode, interesting things like Teyla posing as a Wraith queen and so on. Their "Parallels" ("The Daedalus Variations") seems to be considered the season's best episode.
S5 summed up the series: interesting concepts, fairly good acting/likeable characters, mediocre stories/writing.
Overall, the show had interesting concepts and the actors really made their characters interesting (particularly Joe Flanagan as Sheppard, who managed to make a character as watchable as O'Neill), got them to rise above the phoned in scripts. The Wraith were developed well before the Replicators, and they were starting to get back to developing them when they ended the series. The Genii they should have used far more than they were. Getting rid of the credible faces (Robert Davi, Colm Meaney) hurt them. They needed to be more active because they were interesting villains (should've tried to bring in Avery Brooks as a new Genii captain. Who else would've been a cool Genii?). They neglected the Genii, the Travelers, and overused the Replicators & Michael.
I did not watch SGU. I didn't consider it Stargate and from the information available before it even hit the air, it didn't seem even remotely appealing.
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Watching Stargate, especially from around 2002 or 2003 onward, it seemed clear their writers were borrowing from Star Trek, broad concepts and even being inspired by specific episodes ("This Mortal Coil"= "Course: Oblivion", "Moebius", well it seems to draw from a number of time travel/alternate reality stories, even beyond Star Trek, "Threads" is from some movie, I forget what) and broadly from other works. "Uninvited" is a blatant ripoff of the 1979 film Prophecy. Originality was not their strong suit, especially the writers that joined around the middle of SG1's run, which explains why SGU was such an abomination.